%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:57:43 AM UTC 2026
% Result : Theorem 1.15s 1.47s
% Output : Proof 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 27 unt; 0 def)
% Number of atoms : 123 ( 89 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 136 ( 55 ~; 48 |; 30 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 82 ( 1 sgn 58 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(l32_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('theBenchmark.p',l32_zfmisc_1) ).
fof(t19_zfmisc_1,conjecture,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
file('theBenchmark.p',t19_zfmisc_1) ).
fof(f_2_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_4_2,plain,
! [U_10,U_9,U_8] :
( ( U_8 = unordered_pair(U_10,U_9)
| ? [U_7] :
( ( ~ in(U_7,U_8)
& ( U_7 = U_9
| U_7 = U_10 ) )
| ( U_7 != U_9
& U_7 != U_10
& in(U_7,U_8) ) ) )
& ( ! [U_6] :
( ( in(U_6,U_8)
| ( U_6 != U_9
& U_6 != U_10 ) )
& ( U_6 = U_9
| U_6 = U_10
| ~ in(U_6,U_8) ) )
| U_8 != unordered_pair(U_10,U_9) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ? [U_14] :
( ~ in(U_14,U_16)
& ( U_14 = U_18
| U_14 = U_20 ) )
| ? [U_13] :
( U_13 != U_18
& U_13 != U_20
& in(U_13,U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ? [U_14] :
( ~ in(U_14,U_16)
& ( U_14 = U_18
| U_14 = U_20 ) )
| ( sK1(U_20,U_18,U_16) != U_18
& sK1(U_20,U_18,U_16) != U_20
& in(sK1(U_20,U_18,U_16),U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_13,sK1(U_20,U_18,U_16))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ( ~ in(sK2(U_20,U_18,U_16),U_16)
& ( sK2(U_20,U_18,U_16) = U_18
| sK2(U_20,U_18,U_16) = U_20 ) )
| ( sK1(U_20,U_18,U_16) != U_18
& sK1(U_20,U_18,U_16) != U_20
& in(sK1(U_20,U_18,U_16),U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_20,U_18,U_16))],[f_4_4]) ).
cnf(f_4_8,plain,
( U_12 != U_17
| in(U_12,U_15)
| U_15 != unordered_pair(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_6_1,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l32_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_24,U_23] :
( set_intersection2(U_23,singleton(U_24)) = singleton(U_24)
| ~ in(U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( set_intersection2(U_23,singleton(U_24)) = singleton(U_24)
| ~ in(U_24,U_23) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(negate,[status(cth)],[t19_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) != singleton(A),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_28,U_27] : set_intersection2(singleton(U_28),unordered_pair(U_28,U_27)) != singleton(U_28),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_27] : set_intersection2(singleton(sK5),unordered_pair(sK5,U_27)) != singleton(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_28,sK5)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) != singleton(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) != singleton(sK5),
inference(definitional_conversion,[status(esa)],[f_9_5]) ).
cnf(f_9_7,negated_conjecture,
set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) != singleton(sK5),
inference(clausify,[status(thm)],[f_9_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) != singleton(sK5),
inference(start,[status(thm),parent(0:0)],[f_9_7]) ).
cnf(t2,plain,
( set_intersection2(unordered_pair(sK5,sK6),singleton(sK5)) != singleton(sK5)
| set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) != set_intersection2(unordered_pair(sK5,sK6),singleton(sK5))
| set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) = singleton(sK5) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
set_intersection2(singleton(sK5),unordered_pair(sK5,sK6)) = set_intersection2(unordered_pair(sK5,sK6),singleton(sK5)),
inference(extension,[status(thm),parent(t2:2)],[f_3_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ in(sK5,unordered_pair(sK5,sK6))
| set_intersection2(unordered_pair(sK5,sK6),singleton(sK5)) = singleton(sK5) ),
inference(extension,[status(thm),parent(t2:3)],[f_6_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( sK5 != sK5
| unordered_pair(sK5,sK6) != unordered_pair(sK6,sK5)
| in(sK5,unordered_pair(sK5,sK6)) ),
inference(extension,[status(thm),parent(t6:2)],[f_4_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
unordered_pair(sK5,sK6) = unordered_pair(sK6,sK5),
inference(extension,[status(thm),parent(t8:2)],[f_2_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t8:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:08:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 1.15/1.47 % SZS status Theorem for theBenchmark
% 1.15/1.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------